What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
Submit your PRPs
See the Top discoverers
See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 9001 | 24254^19803+19803^24254 | 104213 | Hans Havermann | 09/2020 |
| 9006 | (10^104212-71)/1 | 104212 | Serge Batalov | 12/2014 |
| 9002 | 2^346182+118065 | 104212 | Stefano Morozzi | 11/2024 |
| 9003 | 2^346184+155085 | 104212 | Stefano Morozzi | 11/2024 |
| 9004 | 2^346184+187513 | 104212 | Stefano Morozzi | 11/2024 |
| 9005 | 2^346184+188455 | 104212 | Stefano Morozzi | 11/2024 |
| 9007 | 2^346180+82735 | 104211 | Stefano Morozzi | 11/2024 |
| 9008 | 2^346180+160593 | 104211 | Stefano Morozzi | 11/2024 |
| 9009 | 2^346180+192333 | 104211 | Stefano Morozzi | 11/2024 |
| 9010 | 2^346181+199821 | 104211 | Stefano Morozzi | 11/2024 |
| 9011 | 2^346176+123667 | 104210 | Stefano Morozzi | 11/2024 |
| 9012 | 2^346178+37455 | 104210 | Stefano Morozzi | 11/2024 |
| 9013 | 2^346178+95865 | 104210 | Stefano Morozzi | 11/2024 |
| 9014 | 2^346178+159517 | 104210 | Stefano Morozzi | 11/2024 |
| 9015 | 2^346174+12543 | 104209 | Stefano Morozzi | 11/2024 |
| 9016 | 2^346169+56049 | 104208 | Stefano Morozzi | 11/2024 |
| 9017 | 2^346169+118965 | 104208 | Stefano Morozzi | 11/2024 |
| 9018 | 2^346170+31363 | 104208 | Stefano Morozzi | 11/2024 |
| 9019 | 2^346165+61767 | 104207 | Stefano Morozzi | 11/2024 |
| 9020 | 2^346166+189919 | 104207 | Stefano Morozzi | 11/2024 |
| 9021 | 2^346167+41681 | 104207 | Stefano Morozzi | 11/2024 |
| 9022 | 2^346162+85765 | 104206 | Stefano Morozzi | 11/2024 |
| 9023 | 2^346164+152925 | 104206 | Stefano Morozzi | 11/2024 |
| 9024 | 2^346160+131703 | 104205 | Stefano Morozzi | 11/2024 |
| 9025 | 2^346155+166433 | 104204 | Stefano Morozzi | 11/2024 |
| 9026 | 2^346157+7137 | 104204 | Stefano Morozzi | 11/2024 |
| 9027 | 2^346158+31483 | 104204 | Stefano Morozzi | 11/2024 |
| 9028 | 2^346158+183253 | 104204 | Stefano Morozzi | 11/2024 |
| 9029 | 2^346152+136287 | 104203 | Stefano Morozzi | 11/2024 |
| 9030 | 2^346154+107499 | 104203 | Stefano Morozzi | 11/2024 |
| 9031 | 2^346154+187987 | 104203 | Stefano Morozzi | 11/2024 |
| 9035 | 23678^23821-23821^23678 | 104202 | Norbert Schneider | 01/2020 |
| 9032 | 2^346149+45857 | 104202 | Stefano Morozzi | 11/2024 |
| 9033 | 2^346150+111579 | 104202 | Stefano Morozzi | 11/2024 |
| 9034 | 2^346151+21539 | 104202 | Stefano Morozzi | 11/2024 |
| 9036 | 2^346143+119183 | 104200 | Stefano Morozzi | 11/2024 |
| 9037 | 2^346143+130361 | 104200 | Stefano Morozzi | 11/2024 |
| 9038 | 2^346143+171791 | 104200 | Stefano Morozzi | 11/2024 |
| 9039 | 2^346144+4731 | 104200 | Stefano Morozzi | 11/2024 |
| 9040 | 2^346144+158097 | 104200 | Stefano Morozzi | 11/2024 |
| 9041 | 2^346139+68459 | 104199 | Stefano Morozzi | 11/2024 |
| 9042 | 2^346140+121711 | 104199 | Stefano Morozzi | 11/2024 |
| 9043 | 2^346135+122913 | 104198 | Stefano Morozzi | 11/2024 |
| 9044 | 2^346135+125453 | 104198 | Stefano Morozzi | 11/2024 |
| 9045 | 2^346135+184869 | 104198 | Stefano Morozzi | 11/2024 |
| 9046 | 2^346136+135721 | 104198 | Stefano Morozzi | 11/2024 |
| 9047 | 2^346133+46695 | 104197 | Stefano Morozzi | 11/2024 |
| 9048 | 2^346129+87819 | 104196 | Stefano Morozzi | 11/2024 |
| 9049 | 2^346130+127369 | 104196 | Stefano Morozzi | 11/2024 |
| 9050 | 2^346130+177619 | 104196 | Stefano Morozzi | 11/2024 |
| 9051 | 2^346125+105609 | 104195 | Stefano Morozzi | 11/2024 |
| 9052 | 2^346127+71201 | 104195 | Stefano Morozzi | 11/2024 |
| 9053 | 2^346122+74469 | 104194 | Stefano Morozzi | 11/2024 |
| 9054 | 2^346122+124119 | 104194 | Stefano Morozzi | 11/2024 |
| 9055 | 2^346122+124227 | 104194 | Stefano Morozzi | 11/2024 |
| 9056 | 2^346124+83973 | 104194 | Stefano Morozzi | 11/2024 |
| 9057 | 2^346124+186877 | 104194 | Stefano Morozzi | 11/2024 |
| 9058 | 2^346121+174729 | 104193 | Stefano Morozzi | 11/2024 |
| 9059 | 2^346116+166317 | 104192 | Stefano Morozzi | 11/2024 |
| 9060 | 2^346117+98015 | 104192 | Stefano Morozzi | 11/2024 |
| 9061 | (13*31^69863+12407)/30 | 104191 | Eric Chen | 04/2024 |
| 9062 | 2^346112+20827 | 104191 | Stefano Morozzi | 11/2024 |
| 9063 | 2^346112+77533 | 104191 | Stefano Morozzi | 11/2024 |
| 9064 | 2^346114+76959 | 104191 | Stefano Morozzi | 11/2024 |
| 9065 | 2^346115+30513 | 104191 | Stefano Morozzi | 11/2024 |
| 9066 | 2^346115+90105 | 104191 | Stefano Morozzi | 11/2024 |
| 9067 | 2^346115+155859 | 104191 | Stefano Morozzi | 11/2024 |
| 9068 | 2^346115+157809 | 104191 | Stefano Morozzi | 11/2024 |
| 9069 | 2^346109+118587 | 104190 | Stefano Morozzi | 11/2024 |
| 9070 | 2^346110+105763 | 104190 | Stefano Morozzi | 11/2024 |
| 9071 | 2^346110+175197 | 104190 | Stefano Morozzi | 11/2024 |
| 9072 | 2^346110+197725 | 104190 | Stefano Morozzi | 11/2024 |
| 9073 | 2^346111+143313 | 104190 | Stefano Morozzi | 11/2024 |
| 9074 | 2^346107+153513 | 104189 | Stefano Morozzi | 11/2024 |
| 9075 | 2^346108+153897 | 104189 | Stefano Morozzi | 11/2024 |
| 9076 | 2^346102+79435 | 104188 | Stefano Morozzi | 11/2024 |
| 9077 | 2^346102+131949 | 104188 | Stefano Morozzi | 11/2024 |
| 9078 | 2^346103+123009 | 104188 | Stefano Morozzi | 11/2024 |
| 9079 | 2^346104+115845 | 104188 | Stefano Morozzi | 11/2024 |
| 9080 | 2^346105+29141 | 104188 | Stefano Morozzi | 11/2024 |
| 9081 | 2^346105+85035 | 104188 | Stefano Morozzi | 11/2024 |
| 9082 | 2^346098+80323 | 104186 | Stefano Morozzi | 11/2024 |
| 9083 | 2^346092+69855 | 104185 | Stefano Morozzi | 11/2024 |
| 9084 | 2^346093+3627 | 104185 | Stefano Morozzi | 11/2024 |
| 9085 | 2^346089+90947 | 104184 | Stefano Morozzi | 11/2024 |
| 9086 | 2^346089+186749 | 104184 | Stefano Morozzi | 11/2024 |
| 9087 | 2^346091+71279 | 104184 | Stefano Morozzi | 11/2024 |
| 9088 | 2^346084+69211 | 104182 | Stefano Morozzi | 11/2024 |
| 9089 | 2^346084+112237 | 104182 | Stefano Morozzi | 11/2024 |
| 9090 | 2^346079+10371 | 104181 | Stefano Morozzi | 11/2024 |
| 9091 | 2^346079+82811 | 104181 | Stefano Morozzi | 11/2024 |
| 9095 | 2^346078+7695 | 104180 | Lelio R Paula | 12/2016 |
| 9092 | 2^346076+85903 | 104180 | Stefano Morozzi | 11/2024 |
| 9093 | 2^346076+111577 | 104180 | Stefano Morozzi | 11/2024 |
| 9094 | 2^346076+143047 | 104180 | Stefano Morozzi | 11/2024 |
| 9096 | 2^346072+126673 | 104179 | Stefano Morozzi | 11/2024 |
| 9097 | 2^346073+37899 | 104179 | Stefano Morozzi | 11/2024 |
| 9098 | 2^346075+21519 | 104179 | Stefano Morozzi | 11/2024 |
| 9099 | 2^346075+27255 | 104179 | Stefano Morozzi | 11/2024 |
| 9100 | 2^346075+115331 | 104179 | Stefano Morozzi | 11/2024 |
| 9101 | 2^346069+53615 | 104178 | Stefano Morozzi | 11/2024 |
| 9102 | 2^346069+188087 | 104178 | Stefano Morozzi | 11/2024 |
| 9103 | 2^346066+29949 | 104177 | Stefano Morozzi | 11/2024 |
| 9104 | 2^346066+133909 | 104177 | Stefano Morozzi | 11/2024 |
| 9105 | 2^346066+188535 | 104177 | Stefano Morozzi | 11/2024 |
| 9106 | 2^346068+159553 | 104177 | Stefano Morozzi | 11/2024 |
| 9107 | 2^346064+122683 | 104176 | Stefano Morozzi | 11/2024 |
| 9108 | 2^346060+20325 | 104175 | Stefano Morozzi | 11/2024 |
| 9109 | 2^346060+110755 | 104175 | Stefano Morozzi | 11/2024 |
| 9110 | 2^346058+57933 | 104174 | Stefano Morozzi | 11/2024 |
| 9116 | 2^346055-19537 | 104173 | Enzo Doria | 05/2013 |
| 9117 | (3*2^346057+1)/77 | 104173 | Lelio R Paula | 12/2013 |
| 9111 | 2^346052+26655 | 104173 | Stefano Morozzi | 11/2024 |
| 9112 | 2^346052+31611 | 104173 | Stefano Morozzi | 11/2024 |
| 9113 | 2^346053+67667 | 104173 | Stefano Morozzi | 11/2024 |
| 9114 | 2^346054+30507 | 104173 | Stefano Morozzi | 11/2024 |
| 9115 | 2^346054+194589 | 104173 | Stefano Morozzi | 11/2024 |
| 9118 | 2^346049+59067 | 104172 | Stefano Morozzi | 11/2024 |
| 9119 | 2^346050+3129 | 104172 | Stefano Morozzi | 11/2024 |
| 9120 | 2^346050+167125 | 104172 | Stefano Morozzi | 11/2024 |
| 9121 | 2^346051+52563 | 104172 | Stefano Morozzi | 11/2024 |
| 9122 | 2^346051+90941 | 104172 | Stefano Morozzi | 11/2024 |
| 9123 | 2^346046+172107 | 104171 | Stefano Morozzi | 11/2024 |
| 9124 | 2^346048+63415 | 104171 | Stefano Morozzi | 11/2024 |
| 9125 | 2^346041+197885 | 104169 | Stefano Morozzi | 11/2024 |
| 9129 | 2^346037-20125 | 104168 | Enzo Doria | 06/2013 |
| 9126 | 2^346036+80773 | 104168 | Stefano Morozzi | 11/2024 |
| 9127 | 2^346037+116429 | 104168 | Stefano Morozzi | 11/2024 |
| 9128 | 2^346038+147549 | 104168 | Stefano Morozzi | 11/2024 |
| 9130 | 2^346034+2205 | 104167 | Stefano Morozzi | 11/2024 |
| 9131 | 2^346031+56429 | 104166 | Stefano Morozzi | 11/2024 |
| 9132 | 2^346031+68439 | 104166 | Stefano Morozzi | 11/2024 |
| 9133 | 2^346031+114891 | 104166 | Stefano Morozzi | 11/2024 |
| 9134 | 2^346031+190563 | 104166 | Stefano Morozzi | 11/2024 |
| 9135 | 2^346026+179305 | 104165 | Stefano Morozzi | 11/2024 |
| 9136 | 2^346027+159425 | 104165 | Stefano Morozzi | 11/2024 |
| 9137 | 2^346028+12517 | 104165 | Stefano Morozzi | 11/2024 |
| 9138 | 2^346022+84705 | 104164 | Stefano Morozzi | 11/2024 |
| 9139 | 2^346019+73673 | 104163 | Stefano Morozzi | 11/2024 |
| 9140 | 2^346019+78999 | 104163 | Stefano Morozzi | 11/2024 |
| 9141 | 2^346019+79955 | 104163 | Stefano Morozzi | 11/2024 |
| 9142 | 2^346020+72993 | 104163 | Stefano Morozzi | 11/2024 |
| 9143 | 2^346020+188673 | 104163 | Stefano Morozzi | 11/2024 |
| 9144 | 2^346021+100311 | 104163 | Stefano Morozzi | 11/2024 |
| 9148 | (34*10^104168-7)/9/13/551179 | 104162 | Makoto Morimoto | 05/2016 |
| 9145 | 2^346016+84007 | 104162 | Stefano Morozzi | 11/2024 |
| 9146 | 2^346017+122397 | 104162 | Stefano Morozzi | 11/2024 |
| 9147 | 2^346017+165791 | 104162 | Stefano Morozzi | 11/2024 |
| 9149 | 2^346014+27949 | 104161 | Stefano Morozzi | 11/2024 |
| 9150 | 2^346014+46743 | 104161 | Stefano Morozzi | 11/2024 |
| 9151 | 2^346015+166089 | 104161 | Stefano Morozzi | 11/2024 |
| 9152 | 2^346009+107705 | 104160 | Stefano Morozzi | 11/2024 |
| 9153 | 2^346012+35043 | 104160 | Stefano Morozzi | 11/2024 |
| 9154 | 2^346012+83091 | 104160 | Stefano Morozzi | 11/2024 |
| 9162 | 6^133854-17993 | 104159 | Enzo Doria | 03/2013 |
| 9155 | 2^346006+77727 | 104159 | Stefano Morozzi | 11/2024 |
| 9156 | 2^346008+9007 | 104159 | Stefano Morozzi | 11/2024 |
| 9157 | 2^346008+51567 | 104159 | Stefano Morozzi | 11/2024 |
| 9158 | 2^346008+107787 | 104159 | Stefano Morozzi | 11/2024 |
| 9159 | 2^346008+146191 | 104159 | Stefano Morozzi | 11/2024 |
| 9160 | 2^346008+170823 | 104159 | Stefano Morozzi | 11/2024 |
| 9161 | (131^49201-1)/7538466025870 | 104159 | Paul Vanderveen | 06/2025 |
| 9163 | 2^346003+191519 | 104158 | Stefano Morozzi | 11/2024 |
| 9164 | 2^345990+1874239 | 104154 | Enzo Doria | 06/2016 |
| 9165 | 2^345988-20373 | 104153 | Enzo Doria | 06/2013 |
| 9166 | (2^345965+2214)/2 | 104146 | Stefano Morozzi | 09/2020 |
| 9167 | 406^39922+405 | 104138 | Alfred Reich | 03/2026 |
| 9168 | (26*10^104132-503)/9 | 104133 | Robert Price | 07/2018 |
| 9169 | 3*5^148968+8 | 104125 | Lelio R Paula | 11/2014 |
| 9170 | (7*10^104113+53)/3 | 104114 | Robert Price | 05/2018 |
| 9171 | p(21253)#/2+8 | 104113 | Robert Price | 01/2017 |
| 9172 | 33582^1259+1259^33582 | 104106 | Hans Havermann | 09/2020 |
| 9173 | 32958^1441+1441^32958 | 104104 | Hans Havermann | 09/2020 |
| 9174 | 29127^3748+3748^29127 | 104095 | Hans Havermann | 09/2020 |
| 9175 | 322^41507+41507^322 | 104094 | Norbert Schneider | 12/2014 |
| 9176 | 6^133768-17423 | 104092 | Enzo Doria | 03/2013 |
| 9177 | 2^345786-19557 | 104092 | Enzo Doria | 05/2013 |
| 9178 | 171^46606-2 | 104072 | Lelio R Paula | 10/2017 |
| 9179 | (29*10^104071+91)/3 | 104072 | Robert Price | 04/2020 |
| 9180 | norm(Mod(x,x^3-x-1)^852167-1) | 104070 | Paul Vanderveen | 09/2022 |
| 9181 | 2^345704-149 | 104068 | Lelio R Paula | 09/2011 |
| 9182 | 25821^10712+10712^25821 | 104056 | Hans Havermann | 09/2020 |
| 9183 | (2^345662+2038)/2 | 104055 | Stefano Morozzi | 09/2020 |
| 9184 | 6^133704-17273 | 104042 | Enzo Doria | 02/2013 |
| 9185 | (3*2^345590-1)/23 | 104033 | Lelio R Paula | 03/2014 |
| 9186 | (19*2^345590+1)/33859 | 104030 | Lelio R Paula | 12/2013 |
| 9187 | 2^345547+11 | 104021 | Lelio R Paula | 09/2011 |
| 9188 | (19*10^104014-49)/3 | 104015 | Robert Price | 05/2019 |
| 9189 | (2^345519+1794)/2 | 104012 | Stefano Morozzi | 01/2021 |
| 9190 | 2^345504+723 | 104008 | Lelio R Paula | 09/2011 |
| 9191 | 2^345498-20037 | 104006 | Enzo Doria | 06/2013 |
| 9193 | 18^82854-37 | 104005 | Lelio R Paula | 01/2017 |
| 9192 | (2^345497+2070)/2 | 104005 | Stefano Morozzi | 09/2020 |
| 9194 | 2^345486-109065 | 104002 | Enzo Doria | 04/2014 |
| 9195 | 2^345487-1851507 | 104002 | Enzo Doria | 08/2015 |
| 9196 | 2^345476+777 | 103999 | Lelio R Paula | 09/2011 |
| 9197 | (2^345477+1554)/2 | 103999 | Stefano Morozzi | 09/2020 |
| 9198 | 4*10^103981-83 | 103982 | Robert Price | 10/2018 |
| 9199 | (2^345327+3206)/2 | 103954 | Stefano Morozzi | 09/2020 |
| 9200 | (5*2^345321-1)/3 | 103953 | Lelio R Paula | 03/2014 |
| 9201 | (2^345267-9)/539049127 | 103927 | Lelio R Paula | 12/2013 |
| 9202 | (19*10^103907+77)/3 | 103908 | Robert Price | 05/2019 |
| 9203 | (78557*2^345163+1)/78589 | 103905 | Lelio R Paula | 07/2014 |
| 9204 | 2^345106-112181 | 103888 | Enzo Doria | 06/2014 |
| 9205 | (2^345105+1326)/2 | 103887 | Stefano Morozzi | 02/2021 |
| 9206 | 2^345079+99 | 103880 | Lelio R Paula | 09/2011 |
| 9207 | (2^345034+1198)/2 | 103866 | Stefano Morozzi | 09/2020 |
| 9208 | 11^99736-1500 | 103865 | Enzo Doria | 12/2012 |
| 9209 | (569^37699-1)/568 | 103863 | Serge Batalov | 06/2022 |
| 9210 | (2^345010+2082)/2 | 103859 | Stefano Morozzi | 09/2020 |
| 9211 | 23263^23784-23784^23263 | 103857 | Norbert Schneider | 01/2020 |
| 9212 | 3*10^103844+31 | 103845 | Robert Price | 06/2021 |
| 9213 | 444*33^68368+19 | 103821 | Eric Chen | 05/2023 |
| 9214 | 23927^21814+21814^23927 | 103813 | Hans Havermann | 09/2020 |
| 9215 | 2^344842-20157 | 103808 | Enzo Doria | 06/2013 |
| 9216 | (47*2^344822+1)/1071 | 103801 | Lelio R Paula | 05/2015 |
| 9217 | 2^344802-20765 | 103796 | Enzo Doria | 06/2013 |
| 9218 | 2^344794-3821 | 103794 | Yves Minet | 05/2011 |
| 9219 | 2^344782-109103 | 103790 | Enzo Doria | 04/2014 |
| 9220 | 3^217521-112292 | 103784 | Enzo Doria | 06/2014 |
| 9221 | 2^344759-3505 | 103783 | Lelio R Paula | 11/2016 |
| 9222 | 2^344735-147 | 103776 | Lelio R Paula | 09/2011 |
| 9223 | L(496533)-p(496533) | 103770 | Robert Price | 02/2018 |
| 9224 | 2*10^103749-69 | 103750 | Robert Price | 03/2018 |
| 9225 | (55459*2^344617+1)/3 | 103745 | Lelio R Paula | 07/2014 |
| 9226 | 2^344607-108891 | 103738 | Enzo Doria | 03/2014 |
| 9228 | (2^344608+3798)/2 | 103738 | Stefano Morozzi | 02/2021 |
| 9227 | (1097^34123-1)/1096 | 103738 | Serge Batalov | 06/2022 |
| 9229 | 2^344560+22411 | 103723 | Enzo Doria | 09/2023 |
| 9230 | (148*10^103718-1)/3 | 103720 | Robert Price | 03/2020 |
| 9231 | 2^344541-19561 | 103718 | Enzo Doria | 05/2013 |
| 9232 | (1017*2^344529-1)/569 | 103714 | Lelio R Paula | 05/2015 |
| 9233 | (8896^26263-1)/8895 | 103714 | Serge Batalov | 06/2022 |
| 9234 | (2^344503+1758)/2 | 103706 | Stefano Morozzi | 09/2020 |
| 9235 | (4*10^103703-1)/3 | 103704 | Serge Batalov | 08/2009 |
| 9236 | 2^344444-455 | 103688 | Yves Minet | 03/2012 |
| 9237 | (4*10^103678-43)/3 | 103679 | Robert Price | 01/2022 |
| 9238 | (13*53^238539*617^9)/10^307661 | 103673 | Hans Havermann | 06/2017 |
| 9239 | (2^344367+2738)/2 | 103665 | Stefano Morozzi | 01/2021 |
| 9241 | 2^344317-109933 | 103650 | Enzo Doria | 04/2014 |
| 9240 | 26055^9508+9508^26055 | 103650 | Hans Havermann | 09/2020 |
| 9242 | 2^344309-1852033 | 103648 | Enzo Doria | 08/2015 |
| 9243 | 25729^10672+10672^25729 | 103643 | Hans Havermann | 09/2020 |
| 9244 | (2^344289+1166)/2 | 103642 | Stefano Morozzi | 09/2020 |
| 9245 | 3*10^103637+61 | 103638 | Robert Price | 09/2020 |
| 9246 | (2^344246+1614)/2 | 103629 | Stefano Morozzi | 09/2020 |
| 9247 | 2^344213-21253 | 103619 | Enzo Doria | 06/2013 |
| 9248 | 2^344196-465 | 103614 | Lelio R Paula | 11/2016 |
| 9249 | 2^344187-20001 | 103611 | Enzo Doria | 06/2013 |
| 9250 | (117191#+(355573#)/(117191#))/(200233679) | 103602 | Makoto Morimoto | 10/2017 |
